Finite Group Databasebeta

← Group #72253021

Character table — Group #72253021

Order 5184.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133
size1111113333666666666666666666888888121212121212121212121212121212181818181818181818181818181818242424243636363636363636363636363636363636363636484848484848484848727272727272727272727272727272727272969696969696969696969696144144144144144144
order123366336644881212121212121212121224242424333666499999912121818181818182666666661212242424243366266666666812122424242424242424121212121212121212363636363636727272727272727272727272999999181818181818363636363636
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111111111111111111111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ311111111111111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111111111111111111111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ4111111111111-1-11111111111-1-1-1-1111111-1111111-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ5111111111111-1-11111111111-1-1-1-1111111-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i32
χ6111111111111-1-11111111111-1-1-1-1111111-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i32
χ7111111−1−i32−1+i32−1−i32−1+i32111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111111111111−1−i32−1+i321−1−i32−1+i32111−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32
χ8111111−1−i32−1+i32−1−i32−1+i32111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111111111111−1−i32−1+i321−1+i321−1−i3211−1−i32−1+i321−1+i321−1−i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i321−1+i321−1−i32−1−i32−1−i32−1+i32−1+i3211−1+i32−1+i3211−1−i32−1−i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i321−1+i321−1−i32
χ9111111−1−i32−1+i32−1−i32−1+i32111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111111111111−1+i321−1−i32−1−i32−1+i32111−1+i321−1−i32−1−i32−1+i321111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1−i32−1+i321−1+i32−1+i3211−1−i32−1−i32−1−i32−1−i32−1+i32−1+i3211−1+i321−1−i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i321
χ10111111−1−i32−1+i32−1−i32−1+i3211-1-111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211-1-1-1-1111111-11−1−i32−1+i321−1−i32−1+i32-1-11−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32-1-1-11+i321+i321+i321−i321−i321−i32-11+i321−i32-1-11+i321+i321+i321−i321−i321−i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-11+i321−i32-11+i321−i32
χ11111111−1−i32−1+i32−1−i32−1+i3211-1-111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211-1-1-1-1111111-1−1−i32−1+i321−1+i321−1−i32-1-1−1−i32−1+i321−1+i321−1−i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32-1-1-11+i321+i321+i321−i321−i321−i32-11+i321−i32-1-11+i321+i321+i321−i321−i321−i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i321−1+i321−1−i321+i321+i321−i321−i32-1-11−i321−i32-1-11+i321+i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i321−1+i321−1−i321+i321−i32-11−i32-11+i32
χ12111111−1−i32−1+i32−1−i32−1+i3211-1-111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211-1-1-1-1111111-1−1+i321−1−i32−1−i32−1+i321-1-1−1+i321−1−i32−1−i32−1+i321111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32-1-1-11+i321+i321+i321−i321−i321−i32-11+i321−i32-1-11+i321+i321+i321−i321−i321−i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1−i32−1+i3211−i321−i32-1-11+i321+i321+i321+i321−i321−i32-1-1−1+i321−1−i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i3211−i32-11+i321+i321−i32-1
χ13111111−1+i32−1−i32−1+i32−1−i32111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111111111111−1+i32−1−i321−1+i32−1−i32111−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32
χ14111111−1+i32−1−i32−1+i32−1−i32111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111111111111−1−i321−1+i32−1+i32−1−i32111−1−i321−1+i32−1+i32−1−i321111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1+i32−1−i321−1−i32−1−i3211−1+i32−1+i32−1+i32−1+i32−1−i32−1−i3211−1−i321−1+i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i321
χ15111111−1+i32−1−i32−1+i32−1−i32111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111111111111−1+i32−1−i321−1−i321−1+i3211−1+i32−1−i321−1−i321−1+i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i321−1−i321−1+i32−1+i32−1+i32−1−i32−1−i3211−1−i32−1−i3211−1+i32−1+i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i321−1−i321−1+i32
χ16111111−1+i32−1−i32−1+i32−1−i3211-1-111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211-1-1-1-1111111-11−1+i32−1−i321−1+i32−1−i32-1-11−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32-1-1-11−i321−i321−i321+i321+i321+i32-11−i321+i32-1-11−i321−i321−i321+i321+i321+i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-11−i321+i32-11−i321+i32
χ17111111−1+i32−1−i32−1+i32−1−i3211-1-111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211-1-1-1-1111111-1−1−i321−1+i32−1+i32−1−i321-1-1−1−i321−1+i32−1+i32−1−i321111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32-1-1-11−i321−i321−i321+i321+i321+i32-11−i321+i32-1-11−i321−i321−i321+i321+i321+i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1+i32−1−i3211+i321+i32-1-11−i321−i321−i321−i321+i321+i32-1-1−1−i321−1+i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i3211+i32-11−i321−i321+i32-1
χ18111111−1+i32−1−i32−1+i32−1−i3211-1-111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211-1-1-1-1111111-1−1+i32−1−i321−1−i321−1+i32-1-1−1+i32−1−i321−1−i321−1+i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32-1-1-11−i321−i321−i321+i321+i321+i32-11−i321+i32-1-11−i321−i321−i321+i321+i321+i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i321−1−i321−1+i321−i321−i321+i321+i32-1-11+i321+i32-1-11−i321−i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i321−1−i321−1+i321−i321+i32-11+i32-11−i32
χ192222222222220022222222220000-1-1-1-1-1-1022222200222222222222222220000-1-1-1-100000000000000000000-1-1-1-1-1-1-1-1-1222222000000000000-1-1-1-1-1-1-1-1-1-1-1-1000000
χ202222222222220022222222220000-1-1-1-1-1-10−1−i3−1−i3−1−i3−1+i3−1+i3−1+i300−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3222222222220000-1-1-1-100000000000000000000-1-1-1-1-1-1-1-1-1−1−i3−1−i3−1−i3−1+i3−1+i3−1+i30000000000001+i321+i321+i321−i321−i321−i321+i321+i321+i321−i321−i321−i32000000
χ212222222222220022222222220000-1-1-1-1-1-10−1+i3−1+i3−1+i3−1−i3−1−i3−1−i300−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3222222222220000-1-1-1-100000000000000000000-1-1-1-1-1-1-1-1-1−1+i3−1+i3−1+i3−1−i3−1−i3−1−i30000000000001−i321−i321−i321+i321+i321+i321−i321−i321−i321+i321+i321+i32000000
χ22222222−1−i3−1+i3−1−i3−1+i3220022−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3220000-1-1-1-1-1-102−1−i3−1+i32−1−i3−1+i3002−1−i3−1+i32−1−i3−1+i3222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1+i300001+i321−i321+i321−i3200000000000000000000-1-1-11+i321+i321+i321−i321−i321−i322−1−i3−1+i32−1−i3−1+i3000000000000-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i32000000
χ23222222−1−i3−1+i3−1−i3−1+i3220022−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3220000-1-1-1-1-1-10−1−i3−1+i32−1+i32−1−i300−1−i3−1+i32−1+i32−1−i3222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1+i300001+i321−i321+i321−i3200000000000000000000-1-1-11+i321+i321+i321−i321−i321−i32−1−i3−1+i32−1+i32−1−i30000000000001+i321−i32-11−i32-11+i321+i321−i32-11−i32-11+i32000000
χ24222222−1−i3−1+i3−1−i3−1+i3220022−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3220000-1-1-1-1-1-10−1+i32−1−i3−1−i3−1+i3200−1+i32−1−i3−1−i3−1+i32222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1+i300001+i321−i321+i321−i3200000000000000000000-1-1-11+i321+i321+i321−i321−i321−i32−1+i32−1−i3−1−i3−1+i320000000000001−i32-11+i321+i321−i32-11−i32-11+i321+i321−i32-1000000
χ25222222−1+i3−1−i3−1+i3−1−i3220022−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3220000-1-1-1-1-1-102−1+i3−1−i32−1+i3−1−i3002−1+i3−1−i32−1+i3−1−i3222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1−i300001−i321+i321−i321+i3200000000000000000000-1-1-11−i321−i321−i321+i321+i321+i322−1+i3−1−i32−1+i3−1−i3000000000000-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i32000000
χ26222222−1+i3−1−i3−1+i3−1−i3220022−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3220000-1-1-1-1-1-10−1−i32−1+i3−1+i3−1−i3200−1−i32−1+i3−1+i3−1−i32222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1−i300001−i321+i321−i321+i3200000000000000000000-1-1-11−i321−i321−i321+i321+i321+i32−1−i32−1+i3−1+i3−1−i320000000000001+i32-11−i321−i321+i32-11+i32-11−i321−i321+i32-1000000
χ27222222−1+i3−1−i3−1+i3−1−i3220022−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3220000-1-1-1-1-1-10−1+i3−1−i32−1−i32−1+i300−1+i3−1−i32−1−i32−1+i3222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1−i300001−i321+i321−i321+i3200000000000000000000-1-1-11−i321−i321−i321+i321+i321+i32−1+i3−1−i32−1−i32−1+i30000000000001−i321+i32-11+i32-11−i321−i321+i32-11+i32-11−i32000000
χ2833333333333-11133333333-1-11111000000-1333333-1-1333333-1-1-1-1-1-1-1-1-1-1-111110000-1-1-1-1-1-1-1-1-11-1-111111111000000000-1-1-1-1-1-1111111111111000000000000-1-1-1-1-1-1
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χ3233333333333-1-1-133333333-1-1-1-1-1-10000001−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i3211−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000111111111-111-1-1-1-1-1-1-1-10000000001+i321+i321+i321−i321−i321−i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32000000000000−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
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χ343333333333-1333-1-1-1-1-1-1-1-1333333333333300000033000000-1-1-1-1-1-1-1-1-13333333333-1-1-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ353333333333-13-3-3-1-1-1-1-1-1-1-133-3-3-3-3333333-3000000-3-3000000-1-1-1-1-1-1-1-1-133-3-3-3-333331111111111-3-311111111-1-1-1-1-1-1-1-1-1000000000000000000000000000000000000
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χ41333333−3−3i32−3+3i32−3−3i32−3+3i323-1-1-133−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32-1-1-1-1-1-10000001−3+3i323−3−3i32−3−3i32−3+3i32311−3+3i323−3−3i32−3−3i32−3+3i323-1-1-11+i321+i321+i321−i321−i321−i321+i321−i321+i321+i321−i321−i320000111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1−1−i32−1+i32-1-11+i321+i321+i321−i321−i321−i320000000001−i32-11+i321+i321−i32-11−i321−i32-1-11+i321+i321+i321+i321−i321−i32-1-1000000000000−1+i321−1−i32−1−i32−1+i321
χ42333333−3−3i32−3+3i32−3−3i32−3+3i32-1333-1-11+i321+i321+i321−i321−i321−i32333333333333300000033000000-1-1-11+i321+i321+i321−i321−i321−i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-1-1-11+i321+i321+i321−i321−i321−i32-1−3−3i32−3+3i32-1-11+i321+i321+i321−i321−i321−i32-1-1-11+i321+i321+i321−i321−i321−i32000000000000000000000000000000000000
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χ48333333−3+3i32−3−3i32−3+3i32−3−3i323-1-1-133−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32-1-1-1-1-1-10000001−3−3i323−3+3i32−3+3i32−3−3i32311−3−3i323−3+3i32−3+3i32−3−3i323-1-1-11−i321−i321−i321+i321+i321+i321−i321+i321−i321−i321+i321+i320000111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1−1+i32−1−i32-1-11−i321−i321−i321+i321+i321+i320000000001+i32-11−i321−i321+i32-11+i321+i32-1-11−i321−i321−i321−i321+i321+i32-1-1000000000000−1−i321−1+i32−1+i32−1−i321
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χ13324-24−12+12i3−12−12i312−12i312+12i300000000000000000000006−3+3i3−3−3i3-63−3i33+3i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.